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+/*
+ * Nearest Points Toy 2
+ *
+ * Authors:
+ * Nathan Hurst <njh at njhurst.com>
+ * Marco Cecchetti <mrcekets at gmail.com>
+ *
+ * Copyright 2008 authors
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it either under the terms of the GNU Lesser General Public
+ * License version 2.1 as published by the Free Software Foundation
+ * (the "LGPL") or, at your option, under the terms of the Mozilla
+ * Public License Version 1.1 (the "MPL"). If you do not alter this
+ * notice, a recipient may use your version of this file under either
+ * the MPL or the LGPL.
+ *
+ * You should have received a copy of the LGPL along with this library
+ * in the file COPYING-LGPL-2.1; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * You should have received a copy of the MPL along with this library
+ * in the file COPYING-MPL-1.1
+ *
+ * The contents of this file are subject to the Mozilla Public License
+ * Version 1.1 (the "License"); you may not use this file except in
+ * compliance with the License. You may obtain a copy of the License at
+ * http://www.mozilla.org/MPL/
+ *
+ * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
+ * OF ANY KIND, either express or implied. See the LGPL or the MPL for
+ * the specific language governing rights and limitations.
+ */
+
+
+#include <2geom/d2.h>
+#include <2geom/sbasis.h>
+#include <2geom/path.h>
+#include <2geom/bezier-to-sbasis.h>
+#include <2geom/sbasis-geometric.h>
+
+#include <toys/path-cairo.h>
+#include <toys/toy-framework.h>
+
+#include <algorithm>
+
+
+using namespace Geom;
+
+
+class np_finder
+{
+public:
+ np_finder(cairo_t* _cr, D2<SBasis> const& _c1, D2<SBasis> const& _c2)
+ : cr(_cr), c1(_c1), c2(_c2)
+ {
+ dc1 = derivative(c1);
+ dc2 = derivative(c2);
+ cd1 = dot(c1,dc1);
+ cd2 = dot(c2,dc2);
+ dsq = 10e30;
+
+ Piecewise<SBasis> k1 = curvature(c1, EPSILON);
+ Piecewise<SBasis> k2 = curvature(c2, EPSILON);
+ Piecewise<SBasis> dk1 = derivative(k1);
+ Piecewise<SBasis> dk2 = derivative(k2);
+ std::vector<double> k1_roots = roots(k1);
+ std::vector<double> k2_roots = roots(k2);
+ std::vector<double> dk1_roots = roots(dk1);
+ std::vector<double> dk2_roots = roots(dk2);
+ tlist.clear();
+ tlist.resize(k1_roots.size() + k2_roots.size() + dk1_roots.size() + dk2_roots.size() + 4);
+ tlist.push_back(0);
+ tlist.insert(tlist.end(), dk1_roots.begin(), dk1_roots.end());
+ tlist.insert(tlist.end(), k1_roots.begin(), k1_roots.end());
+// std::cerr << "dk1 roots: ";
+// for ( unsigned int i = 0; i < dk1_roots.size(); ++i )
+// {
+// std::cerr << dk1_roots[i] << " ";
+// }
+// std::cerr << "\n";
+ for ( unsigned int i = 0; i < k2_roots.size(); ++i )
+ {
+ tlist.push_back(nearest_time(c2(k2_roots[i]), c1, dc1, cd1));
+ }
+
+ for ( unsigned int i = 0; i < dk2_roots.size(); ++i )
+ {
+ tlist.push_back(nearest_time(c2(dk2_roots[i]), c1, dc1, cd1));
+ }
+ tlist.push_back(nearest_time(c2(0), c1, dc1, cd1));
+ tlist.push_back(nearest_time(c2(1), c1, dc1, cd1));
+ tlist.push_back(1);
+ std::sort(tlist.begin(), tlist.end());
+ std::vector<double>::iterator pos
+ = std::unique(tlist.begin(), tlist.end(), are_near_() );
+ if (pos != tlist.end())
+ {
+ tlist.erase(pos, tlist.end());
+ }
+ for( unsigned int i = 0; i < tlist.size(); ++i )
+ {
+ draw_circ(cr, c1(tlist[i]) );
+ }
+ }
+
+ void operator() ()
+ {
+ //nearest_times_impl( tlist.size() / 2, 0, tlist.size() - 1 );
+ nearest_times_impl();
+ d = sqrt(dsq);
+ }
+
+ Point firstPoint() const
+ {
+ return p1;
+ }
+
+ Point secondPoint() const
+ {
+ return p2;
+ }
+
+ double firstValue() const
+ {
+ return t1;
+ }
+
+ double secondValue() const
+ {
+ return t2;
+ }
+
+ double distance() const
+ {
+ return d;
+ }
+
+private:
+ void nearest_times_impl()
+ {
+ double t;
+ double from = tlist[0];
+ double to;
+ for ( unsigned int i = 1; i < tlist.size(); ++i )
+ {
+ to = tlist[i];
+ t = from + (to - from) / 2 ;
+ std::pair<double, double> npc = loc_nearest_times(t, from, to);
+ if ( npc.second != -1 && dsq > L2sq(c1(npc.first) - c2(npc.second)) )
+ {
+ t1 = npc.first;
+ t2 = npc.second;
+ p1 = c1(t1);
+ p2 = c2(t2);
+ dsq = L2sq(p1 - p2);
+ }
+ from = tlist[i];
+ }
+ }
+
+ std::pair<double, double>
+ loc_nearest_times( double t, double from = 0, double to = 1 )
+ {
+ //std::cerr << "[" << from << "," << to << "] t: " << t << std::endl;
+ unsigned int i = 0;
+ std::pair<double, double> np(-1,-1);
+ std::pair<double, double> npf(from, -1);
+ std::pair<double, double> npt(to, -1);
+ double ct = t;
+ double pt = -1;
+ double s;
+ //cairo_set_source_rgba(cr, 1/(t+1), t*t, t, 1.0);
+ cairo_move_to(cr, c1(t));
+ while( !are_near(ct, pt) )
+ {
+ ++i;
+ pt = ct;
+ s = nearest_time(c1(ct), c2, dc2, cd2);
+ //std::cerr << "s: " << s << std::endl;
+ //cairo_line_to(cr, c2(s));
+ ct = nearest_time(c2(s), c1, dc1, cd1, from, to);
+ //std::cerr << "t: " << ct << std::endl;
+ //cairo_line_to(cr, c1(ct));
+ //std::cerr << "d(pt, ct) = " << std::fabs(ct - pt) << std::endl;
+ if ( ct < from ) return npf;
+ if ( ct > to ) return npt;
+ }
+ //std::cerr << "\n \n";
+ std::cerr << "iterations: " << i << std::endl;
+ //cairo_move_to(cr, c1(ct));
+ //cairo_line_to(cr, c2(s));
+ cairo_stroke(cr);
+ np.first = ct;
+ np.second = s;
+ return np;
+ }
+
+ double nearest_time( Point const& p, D2<SBasis> const&c, D2<SBasis> const& dc, SBasis const& cd, double from = 0, double to = 1 )
+ {
+ D2<SBasis> sbc = c - p;
+ SBasis dd = cd - dotp(p, dc);
+ std::vector<double> zeros = roots(dd);
+ double closest = from;
+ double distsq = L2sq(sbc(from));
+ for ( unsigned int i = 0; i < zeros.size(); ++i )
+ {
+ if ( distsq > L2sq(sbc(zeros[i])) )
+ {
+ closest = zeros[i];
+ distsq = L2sq(sbc(closest));
+ }
+ }
+ if ( distsq > L2sq(sbc(to)) )
+ closest = to;
+ return closest;
+ }
+
+ SBasis dotp(Point const& p, D2<SBasis> const& c)
+ {
+ SBasis d;
+ d.resize(c[X].size());
+ for ( unsigned int i = 0; i < c[0].size(); ++i )
+ {
+ for( unsigned int j = 0; j < 2; ++j )
+ d[i][j] = p[X] * c[X][i][j] + p[Y] * c[Y][i][j];
+ }
+ return d;
+ }
+
+ struct are_near_
+ {
+ bool operator() (double x, double y, double eps = Geom::EPSILON )
+ {
+ return are_near(x, y, eps);
+ }
+ };
+
+private:
+ static const Coord EPSILON = 10e-5;
+ cairo_t* cr;
+ D2<SBasis> const& c1, c2;
+ D2<SBasis> dc1, dc2;
+ SBasis cd1, cd2;
+ double t1, t2, d, dsq;
+ Point p1, p2;
+ std::vector<double> tlist;
+};
+
+
+
+
+class NearestPoints : public Toy
+{
+ private:
+ void draw( cairo_t *cr, std::ostringstream *notify,
+ int width, int height, bool save, std::ostringstream *timer_stream)
+ {
+ cairo_set_line_width (cr, 0.2);
+ D2<SBasis> A = handles_to_sbasis(handles.begin(), A_bez_ord-1);
+ cairo_d2_sb(cr, A);
+ D2<SBasis> B = handles_to_sbasis(handles.begin()+A_bez_ord, B_bez_ord-1);
+ cairo_d2_sb(cr, B);
+
+
+ np_finder np(cr, A, B);
+ np();
+ cairo_move_to(cr, np.firstPoint());
+ cairo_line_to(cr, np.secondPoint());
+ cairo_stroke(cr);
+ //std::cerr << "np: (" << np.firstValue() << "," << np.secondValue() << ")" << std::endl;
+
+ Toy::draw(cr, notify, width, height, save,timer_stream);
+ }
+
+ public:
+ NearestPoints(unsigned int _A_bez_ord, unsigned int _B_bez_ord)
+ : A_bez_ord(_A_bez_ord), B_bez_ord(_B_bez_ord)
+ {
+ unsigned int total_handles = A_bez_ord + B_bez_ord;
+ for ( unsigned int i = 0; i < total_handles; ++i )
+ handles.push_back(Geom::Point(uniform()*400, uniform()*400));
+ }
+
+ private:
+ unsigned int A_bez_ord;
+ unsigned int B_bez_ord;
+};
+
+
+int main(int argc, char **argv)
+{
+ unsigned int A_bez_ord=8;
+ unsigned int B_bez_ord=5;
+ if(argc > 2)
+ sscanf(argv[2], "%d", &B_bez_ord);
+ if(argc > 1)
+ sscanf(argv[1], "%d", &A_bez_ord);
+
+ init( argc, argv, new NearestPoints(A_bez_ord, B_bez_ord));
+ return 0;
+}
+
+
+/*
+ Local Variables:
+ mode:c++
+ c-file-style:"stroustrup"
+ c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
+ indent-tabs-mode:nil
+ fill-column:99
+ End:
+*/
+// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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